Answer
Verified
91.5k+ views
Hint: Assume that the number of books bought by Aniruddha equals ‘n’. He bought ‘n’ books for Rs 60. So, the price of each book is $\dfrac{60}{n}$. It is given that if he had bought 5 more books i.e. ‘n+5’ books for the same price i.e. Rs 60, each book would have cost him Rs. $\dfrac{60}{n+5}$.
Using this data and the information given in the question, solve for ‘n’.
Let us assume that Aniruddha has bought n books. In the question, it is given that he bought this book for Rs. 60. So, the price of each book will be equal to Rs $\dfrac{60}{n}........\left( 1 \right)$.
If he would have bought 5 more books i.e. n+5 books for the same price i.e. Rs 60, the price of each book will be equal to $\dfrac{60}{n+5}...........\left( 2 \right)$
Also, it is given in the question that if he would have 5 more books i.e. n+5 books for the same price i.e. Rs 60, each book would have cost him 1 rupee less.
Using equation $\left( 1 \right)$ and $\left( 2 \right)$ and the information mention in the above paragraph, we get,
$\begin{align}
& \dfrac{60}{n}-1=\dfrac{60}{n+5} \\
& \Rightarrow \dfrac{60-n}{n}=\dfrac{60}{n+5} \\
& \Rightarrow \left( 60-n \right)\left( n+5 \right)=60n \\
& \Rightarrow 60n+300-{{n}^{2}}-5n=60n \\
& \Rightarrow {{n}^{2}}+5n-300=0 \\
& \Rightarrow {{n}^{2}}-15n+20n-300=0 \\
& \Rightarrow n\left( n-15 \right)+20\left( n-15 \right)=0 \\
& \Rightarrow \left( n-15 \right)\left( n+20 \right)=0 \\
& \Rightarrow n=15,n=-20 \\
\end{align}$
Since n represents the number of books, so, it must be positive.
$\Rightarrow n=15$
Hence, the answer is 15.
Note: There is a possibility that one may commit a mistake by writing the equation as
$\dfrac{60}{n}=\dfrac{60}{n+5}-1$ instead of $\dfrac{60}{n}-1=\dfrac{60}{n+5}$. So, one should read this question very carefully in order to obtain the correct equation and the correct answer.
Using this data and the information given in the question, solve for ‘n’.
Let us assume that Aniruddha has bought n books. In the question, it is given that he bought this book for Rs. 60. So, the price of each book will be equal to Rs $\dfrac{60}{n}........\left( 1 \right)$.
If he would have bought 5 more books i.e. n+5 books for the same price i.e. Rs 60, the price of each book will be equal to $\dfrac{60}{n+5}...........\left( 2 \right)$
Also, it is given in the question that if he would have 5 more books i.e. n+5 books for the same price i.e. Rs 60, each book would have cost him 1 rupee less.
Using equation $\left( 1 \right)$ and $\left( 2 \right)$ and the information mention in the above paragraph, we get,
$\begin{align}
& \dfrac{60}{n}-1=\dfrac{60}{n+5} \\
& \Rightarrow \dfrac{60-n}{n}=\dfrac{60}{n+5} \\
& \Rightarrow \left( 60-n \right)\left( n+5 \right)=60n \\
& \Rightarrow 60n+300-{{n}^{2}}-5n=60n \\
& \Rightarrow {{n}^{2}}+5n-300=0 \\
& \Rightarrow {{n}^{2}}-15n+20n-300=0 \\
& \Rightarrow n\left( n-15 \right)+20\left( n-15 \right)=0 \\
& \Rightarrow \left( n-15 \right)\left( n+20 \right)=0 \\
& \Rightarrow n=15,n=-20 \\
\end{align}$
Since n represents the number of books, so, it must be positive.
$\Rightarrow n=15$
Hence, the answer is 15.
Note: There is a possibility that one may commit a mistake by writing the equation as
$\dfrac{60}{n}=\dfrac{60}{n+5}-1$ instead of $\dfrac{60}{n}-1=\dfrac{60}{n+5}$. So, one should read this question very carefully in order to obtain the correct equation and the correct answer.
Recently Updated Pages
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main
Other Pages
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
3 mole of gas X and 2 moles of gas Y enters from the class 11 physics JEE_Main
The vapour pressure of pure A is 10 torr and at the class 12 chemistry JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
If the central portion of a convex lens is wrapped class 12 physics JEE_Main